/*

  * Copyright (c) 1997, 2011, Oracle and/or its affiliates. All rights reserved.

  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

  *

  * This code is free software; you can redistribute it and/or modify it

  * under the terms of the GNU General Public License version 2 only, as

  * published by the Free Software Foundation.  Oracle designates this

  * particular file as subject to the "Classpath" exception as provided

  * by Oracle in the LICENSE file that accompanied this code.

  *

  * This code is distributed in the hope that it will be useful, but WITHOUT

  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

  * version 2 for more details (a copy is included in the LICENSE file that

  * accompanied this code).

  *

  * You should have received a copy of the GNU General Public License version

  * 2 along with this work; if not, write to the Free Software Foundation,

  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

  *

  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

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  * questions.

  */

 package java.util;

 import java.lang.reflect.*;

 /**

  * This class contains various methods for manipulating arrays (such as

  * sorting and searching). This class also contains a static factory

  * that allows arrays to be viewed as lists.

  *

  * <p>The methods in this class all throw a {@code NullPointerException},

  * if the specified array reference is null, except where noted.

  *

  * <p>The documentation for the methods contained in this class includes

  * briefs description of the <i>implementations</i>. Such descriptions should

  * be regarded as <i>implementation notes</i>, rather than parts of the

  * <i>specification</i>. Implementors should feel free to substitute other

  * algorithms, so long as the specification itself is adhered to. (For

  * example, the algorithm used by {@code sort(Object[])} does not have to be

  * a MergeSort, but it does have to be <i>stable</i>.)

  *

  * <p>This class is a member of the

  * <a href="{@docRoot}/../technotes/guides/collections/index.html">

  * Java Collections Framework</a>.

  *

  * @author Josh Bloch

  * @author Neal Gafter

  * @author John Rose

  * @since  1.2

  */

 public class Arrays {

     // Suppresses default constructor, ensuring non-instantiability.

     private Arrays() {}

     /*

      * Sorting of primitive type arrays.

      */

     /**

      * Sorts the specified array into ascending numerical order.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      */

     public static void sort(int[] a) {

         DualPivotQuicksort.sort(a);

     }

     /**

      * Sorts the specified range of the array into ascending order. The range

      * to be sorted extends from the index {@code fromIndex}, inclusive, to

      * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},

      * the range to be sorted is empty.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element, inclusive, to be sorted

      * @param toIndex the index of the last element, exclusive, to be sorted

      *

      * @throws IllegalArgumentException if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *     if {@code fromIndex < 0} or {@code toIndex > a.length}

      */

     public static void sort(int[] a, int fromIndex, int toIndex) {

         rangeCheck(a.length, fromIndex, toIndex);

         DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);

     }

     /**

      * Sorts the specified array into ascending numerical order.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      */

     public static void sort(long[] a) {

         DualPivotQuicksort.sort(a);

     }

     /**

      * Sorts the specified range of the array into ascending order. The range

      * to be sorted extends from the index {@code fromIndex}, inclusive, to

      * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},

      * the range to be sorted is empty.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element, inclusive, to be sorted

      * @param toIndex the index of the last element, exclusive, to be sorted

      *

      * @throws IllegalArgumentException if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *     if {@code fromIndex < 0} or {@code toIndex > a.length}

      */

     public static void sort(long[] a, int fromIndex, int toIndex) {

         rangeCheck(a.length, fromIndex, toIndex);

         DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);

     }

     /**

      * Sorts the specified array into ascending numerical order.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      */

     public static void sort(short[] a) {

         DualPivotQuicksort.sort(a);

     }

     /**

      * Sorts the specified range of the array into ascending order. The range

      * to be sorted extends from the index {@code fromIndex}, inclusive, to

      * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},

      * the range to be sorted is empty.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element, inclusive, to be sorted

      * @param toIndex the index of the last element, exclusive, to be sorted

      *

      * @throws IllegalArgumentException if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *     if {@code fromIndex < 0} or {@code toIndex > a.length}

      */

     public static void sort(short[] a, int fromIndex, int toIndex) {

         rangeCheck(a.length, fromIndex, toIndex);

         DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);

     }

     /**

      * Sorts the specified array into ascending numerical order.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      */

     public static void sort(char[] a) {

         DualPivotQuicksort.sort(a);

     }

     /**

      * Sorts the specified range of the array into ascending order. The range

      * to be sorted extends from the index {@code fromIndex}, inclusive, to

      * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},

      * the range to be sorted is empty.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element, inclusive, to be sorted

      * @param toIndex the index of the last element, exclusive, to be sorted

      *

      * @throws IllegalArgumentException if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *     if {@code fromIndex < 0} or {@code toIndex > a.length}

      */

     public static void sort(char[] a, int fromIndex, int toIndex) {

         rangeCheck(a.length, fromIndex, toIndex);

         DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);

     }

     /**

      * Sorts the specified array into ascending numerical order.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      */

     public static void sort(byte[] a) {

         DualPivotQuicksort.sort(a);

     }

     /**

      * Sorts the specified range of the array into ascending order. The range

      * to be sorted extends from the index {@code fromIndex}, inclusive, to

      * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},

      * the range to be sorted is empty.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element, inclusive, to be sorted

      * @param toIndex the index of the last element, exclusive, to be sorted

      *

      * @throws IllegalArgumentException if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *     if {@code fromIndex < 0} or {@code toIndex > a.length}

      */

     public static void sort(byte[] a, int fromIndex, int toIndex) {

         rangeCheck(a.length, fromIndex, toIndex);

         DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);

     }

     /**

      * Sorts the specified array into ascending numerical order.

      *

      * <p>The {@code <} relation does not provide a total order on all float

      * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}

      * value compares neither less than, greater than, nor equal to any value,

      * even itself. This method uses the total order imposed by the method

      * {@link Float#compareTo}: {@code -0.0f} is treated as less than value

      * {@code 0.0f} and {@code Float.NaN} is considered greater than any

      * other value and all {@code Float.NaN} values are considered equal.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      */

     public static void sort(float[] a) {

         DualPivotQuicksort.sort(a);

     }

     /**

      * Sorts the specified range of the array into ascending order. The range

      * to be sorted extends from the index {@code fromIndex}, inclusive, to

      * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},

      * the range to be sorted is empty.

      *

      * <p>The {@code <} relation does not provide a total order on all float

      * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}

      * value compares neither less than, greater than, nor equal to any value,

      * even itself. This method uses the total order imposed by the method

      * {@link Float#compareTo}: {@code -0.0f} is treated as less than value

      * {@code 0.0f} and {@code Float.NaN} is considered greater than any

      * other value and all {@code Float.NaN} values are considered equal.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element, inclusive, to be sorted

      * @param toIndex the index of the last element, exclusive, to be sorted

      *

      * @throws IllegalArgumentException if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *     if {@code fromIndex < 0} or {@code toIndex > a.length}

      */

     public static void sort(float[] a, int fromIndex, int toIndex) {

         rangeCheck(a.length, fromIndex, toIndex);

         DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);

     }

     /**

      * Sorts the specified array into ascending numerical order.

      *

      * <p>The {@code <} relation does not provide a total order on all double

      * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}

      * value compares neither less than, greater than, nor equal to any value,

      * even itself. This method uses the total order imposed by the method

      * {@link Double#compareTo}: {@code -0.0d} is treated as less than value

      * {@code 0.0d} and {@code Double.NaN} is considered greater than any

      * other value and all {@code Double.NaN} values are considered equal.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      */

     public static void sort(double[] a) {

         DualPivotQuicksort.sort(a);

     }

     /**

      * Sorts the specified range of the array into ascending order. The range

      * to be sorted extends from the index {@code fromIndex}, inclusive, to

      * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},

      * the range to be sorted is empty.

      *

      * <p>The {@code <} relation does not provide a total order on all double

      * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}

      * value compares neither less than, greater than, nor equal to any value,

      * even itself. This method uses the total order imposed by the method

      * {@link Double#compareTo}: {@code -0.0d} is treated as less than value

      * {@code 0.0d} and {@code Double.NaN} is considered greater than any

      * other value and all {@code Double.NaN} values are considered equal.

      *

      * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort

      * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm

      * offers O(n log(n)) performance on many data sets that cause other

      * quicksorts to degrade to quadratic performance, and is typically

      * faster than traditional (one-pivot) Quicksort implementations.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element, inclusive, to be sorted

      * @param toIndex the index of the last element, exclusive, to be sorted

      *

      * @throws IllegalArgumentException if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *     if {@code fromIndex < 0} or {@code toIndex > a.length}

      */

     public static void sort(double[] a, int fromIndex, int toIndex) {

         rangeCheck(a.length, fromIndex, toIndex);

         DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);

     }

     /*

      * Sorting of complex type arrays.

      */

     /**

      * Old merge sort implementation can be selected (for

      * compatibility with broken comparators) using a system property.

      * Cannot be a static boolean in the enclosing class due to

      * circular dependencies. To be removed in a future release.

      */

     static final class LegacyMergeSort {

         private static final boolean userRequested = false;

     }

     /*

      * If this platform has an optimizing VM, check whether ComparableTimSort

      * offers any performance benefit over TimSort in conjunction with a

      * comparator that returns:

      *    {@code ((Comparable)first).compareTo(Second)}.

      * If not, you are better off deleting ComparableTimSort to

      * eliminate the code duplication.  In other words, the commented

      * out code below is the preferable implementation for sorting

      * arrays of Comparables if it offers sufficient performance.

      */

 //    /**

 //     * A comparator that implements the natural ordering of a group of

 //     * mutually comparable elements.  Using this comparator saves us

 //     * from duplicating most of the code in this file (one version for

 //     * Comparables, one for explicit Comparators).

 //     */

 //    private static final Comparator<Object> NATURAL_ORDER =

 //            new Comparator<Object>() {

 //        @SuppressWarnings("unchecked")

 //        public int compare(Object first, Object second) {

 //            return ((Comparable<Object>)first).compareTo(second);

 //        }

 //    };

 //

 //    public static void sort(Object[] a) {

 //        sort(a, 0, a.length, NATURAL_ORDER);

 //    }

 //

 //    public static void sort(Object[] a, int fromIndex, int toIndex) {

 //        sort(a, fromIndex, toIndex, NATURAL_ORDER);

 //    }

     /**

      * Sorts the specified array of objects into ascending order, according

      * to the {@linkplain Comparable natural ordering} of its elements.

      * All elements in the array must implement the {@link Comparable}

      * interface.  Furthermore, all elements in the array must be

      * <i>mutually comparable</i> (that is, {@code e1.compareTo(e2)} must

      * not throw a {@code ClassCastException} for any elements {@code e1}

      * and {@code e2} in the array).

      *

      * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will

      * not be reordered as a result of the sort.

      *

      * <p>Implementation note: This implementation is a stable, adaptive,

      * iterative mergesort that requires far fewer than n lg(n) comparisons

      * when the input array is partially sorted, while offering the

      * performance of a traditional mergesort when the input array is

      * randomly ordered.  If the input array is nearly sorted, the

      * implementation requires approximately n comparisons.  Temporary

      * storage requirements vary from a small constant for nearly sorted

      * input arrays to n/2 object references for randomly ordered input

      * arrays.

      *

      * <p>The implementation takes equal advantage of ascending and

      * descending order in its input array, and can take advantage of

      * ascending and descending order in different parts of the the same

      * input array.  It is well-suited to merging two or more sorted arrays:

      * simply concatenate the arrays and sort the resulting array.

      *

      * <p>The implementation was adapted from Tim Peters's list sort for Python

      * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">

      * TimSort</a>).  It uses techiques from Peter McIlroy's "Optimistic

      * Sorting and Information Theoretic Complexity", in Proceedings of the

      * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,

      * January 1993.

      *

      * @param a the array to be sorted

      * @throws ClassCastException if the array contains elements that are not

      *         <i>mutually comparable</i> (for example, strings and integers)

      * @throws IllegalArgumentException (optional) if the natural

      *         ordering of the array elements is found to violate the

      *         {@link Comparable} contract

      */

     public static void sort(Object[] a) {

         if (LegacyMergeSort.userRequested)

             legacyMergeSort(a);

         else

             ComparableTimSort.sort(a);

     }

     /** To be removed in a future release. */

     private static void legacyMergeSort(Object[] a) {

         Object[] aux = a.clone();

         mergeSort(aux, a, 0, a.length, 0);

     }

     /**

      * Sorts the specified range of the specified array of objects into

      * ascending order, according to the

      * {@linkplain Comparable natural ordering} of its

      * elements.  The range to be sorted extends from index

      * {@code fromIndex}, inclusive, to index {@code toIndex}, exclusive.

      * (If {@code fromIndex==toIndex}, the range to be sorted is empty.)  All

      * elements in this range must implement the {@link Comparable}

      * interface.  Furthermore, all elements in this range must be <i>mutually

      * comparable</i> (that is, {@code e1.compareTo(e2)} must not throw a

      * {@code ClassCastException} for any elements {@code e1} and

      * {@code e2} in the array).

      *

      * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will

      * not be reordered as a result of the sort.

      *

      * <p>Implementation note: This implementation is a stable, adaptive,

      * iterative mergesort that requires far fewer than n lg(n) comparisons

      * when the input array is partially sorted, while offering the

      * performance of a traditional mergesort when the input array is

      * randomly ordered.  If the input array is nearly sorted, the

      * implementation requires approximately n comparisons.  Temporary

      * storage requirements vary from a small constant for nearly sorted

      * input arrays to n/2 object references for randomly ordered input

      * arrays.

      *

      * <p>The implementation takes equal advantage of ascending and

      * descending order in its input array, and can take advantage of

      * ascending and descending order in different parts of the the same

      * input array.  It is well-suited to merging two or more sorted arrays:

      * simply concatenate the arrays and sort the resulting array.

      *

      * <p>The implementation was adapted from Tim Peters's list sort for Python

      * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">

      * TimSort</a>).  It uses techiques from Peter McIlroy's "Optimistic

      * Sorting and Information Theoretic Complexity", in Proceedings of the

      * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,

      * January 1993.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element (inclusive) to be

      *        sorted

      * @param toIndex the index of the last element (exclusive) to be sorted

      * @throws IllegalArgumentException if {@code fromIndex > toIndex} or

      *         (optional) if the natural ordering of the array elements is

      *         found to violate the {@link Comparable} contract

      * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or

      *         {@code toIndex > a.length}

      * @throws ClassCastException if the array contains elements that are

      *         not <i>mutually comparable</i> (for example, strings and

      *         integers).

      */

     public static void sort(Object[] a, int fromIndex, int toIndex) {

         if (LegacyMergeSort.userRequested)

             legacyMergeSort(a, fromIndex, toIndex);

         else

             ComparableTimSort.sort(a, fromIndex, toIndex);

     }

     /** To be removed in a future release. */

     private static void legacyMergeSort(Object[] a,

                                         int fromIndex, int toIndex) {

         rangeCheck(a.length, fromIndex, toIndex);

         Object[] aux = copyOfRange(a, fromIndex, toIndex);

         mergeSort(aux, a, fromIndex, toIndex, -fromIndex);

     }

     /**

      * Tuning parameter: list size at or below which insertion sort will be

      * used in preference to mergesort.

      * To be removed in a future release.

      */

     private static final int INSERTIONSORT_THRESHOLD = 7;

     /**

      * Src is the source array that starts at index 0

      * Dest is the (possibly larger) array destination with a possible offset

      * low is the index in dest to start sorting

      * high is the end index in dest to end sorting

      * off is the offset to generate corresponding low, high in src

      * To be removed in a future release.

      */

     private static void mergeSort(Object[] src,

                                   Object[] dest,

                                   int low,

                                   int high,

                                   int off) {

         int length = high - low;

         // Insertion sort on smallest arrays

         if (length < INSERTIONSORT_THRESHOLD) {

             for (int i=low; i<high; i++)

                 for (int j=i; j>low &&

                          ((Comparable) dest[j-1]).compareTo(dest[j])>0; j--)

                     swap(dest, j, j-1);

             return;

         }

         // Recursively sort halves of dest into src

         int destLow  = low;

         int destHigh = high;

         low  += off;

         high += off;

         int mid = (low + high) >>> 1;

         mergeSort(dest, src, low, mid, -off);

         mergeSort(dest, src, mid, high, -off);

         // If list is already sorted, just copy from src to dest.  This is an

         // optimization that results in faster sorts for nearly ordered lists.

         if (((Comparable)src[mid-1]).compareTo(src[mid]) <= 0) {

             System.arraycopy(src, low, dest, destLow, length);

             return;

         }

         // Merge sorted halves (now in src) into dest

         for(int i = destLow, p = low, q = mid; i < destHigh; i++) {

             if (q >= high || p < mid && ((Comparable)src[p]).compareTo(src[q])<=0)

                 dest[i] = src[p++];

             else

                 dest[i] = src[q++];

         }

     }

     /**

      * Swaps x[a] with x[b].

      */

     private static void swap(Object[] x, int a, int b) {

         Object t = x[a];

         x[a] = x[b];

         x[b] = t;

     }

     /**

      * Sorts the specified array of objects according to the order induced by

      * the specified comparator.  All elements in the array must be

      * <i>mutually comparable</i> by the specified comparator (that is,

      * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}

      * for any elements {@code e1} and {@code e2} in the array).

      *

      * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will

      * not be reordered as a result of the sort.

      *

      * <p>Implementation note: This implementation is a stable, adaptive,

      * iterative mergesort that requires far fewer than n lg(n) comparisons

      * when the input array is partially sorted, while offering the

      * performance of a traditional mergesort when the input array is

      * randomly ordered.  If the input array is nearly sorted, the

      * implementation requires approximately n comparisons.  Temporary

      * storage requirements vary from a small constant for nearly sorted

      * input arrays to n/2 object references for randomly ordered input

      * arrays.

      *

      * <p>The implementation takes equal advantage of ascending and

      * descending order in its input array, and can take advantage of

      * ascending and descending order in different parts of the the same

      * input array.  It is well-suited to merging two or more sorted arrays:

      * simply concatenate the arrays and sort the resulting array.

      *

      * <p>The implementation was adapted from Tim Peters's list sort for Python

      * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">

      * TimSort</a>).  It uses techiques from Peter McIlroy's "Optimistic

      * Sorting and Information Theoretic Complexity", in Proceedings of the

      * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,

      * January 1993.

      *

      * @param a the array to be sorted

      * @param c the comparator to determine the order of the array.  A

      *        {@code null} value indicates that the elements'

      *        {@linkplain Comparable natural ordering} should be used.

      * @throws ClassCastException if the array contains elements that are

      *         not <i>mutually comparable</i> using the specified comparator

      * @throws IllegalArgumentException (optional) if the comparator is

      *         found to violate the {@link Comparator} contract

      */

     public static <T> void sort(T[] a, Comparator<? super T> c) {

         if (LegacyMergeSort.userRequested)

             legacyMergeSort(a, c);

         else

             TimSort.sort(a, c);

     }

     /** To be removed in a future release. */

     private static <T> void legacyMergeSort(T[] a, Comparator<? super T> c) {

         T[] aux = a.clone();

         if (c==null)

             mergeSort(aux, a, 0, a.length, 0);

         else

             mergeSort(aux, a, 0, a.length, 0, c);

     }

     /**

      * Sorts the specified range of the specified array of objects according

      * to the order induced by the specified comparator.  The range to be

      * sorted extends from index {@code fromIndex}, inclusive, to index

      * {@code toIndex}, exclusive.  (If {@code fromIndex==toIndex}, the

      * range to be sorted is empty.)  All elements in the range must be

      * <i>mutually comparable</i> by the specified comparator (that is,

      * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}

      * for any elements {@code e1} and {@code e2} in the range).

      *

      * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will

      * not be reordered as a result of the sort.

      *

      * <p>Implementation note: This implementation is a stable, adaptive,

      * iterative mergesort that requires far fewer than n lg(n) comparisons

      * when the input array is partially sorted, while offering the

      * performance of a traditional mergesort when the input array is

      * randomly ordered.  If the input array is nearly sorted, the

      * implementation requires approximately n comparisons.  Temporary

      * storage requirements vary from a small constant for nearly sorted

      * input arrays to n/2 object references for randomly ordered input

      * arrays.

      *

      * <p>The implementation takes equal advantage of ascending and

      * descending order in its input array, and can take advantage of

      * ascending and descending order in different parts of the the same

      * input array.  It is well-suited to merging two or more sorted arrays:

      * simply concatenate the arrays and sort the resulting array.

      *

      * <p>The implementation was adapted from Tim Peters's list sort for Python

      * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">

      * TimSort</a>).  It uses techiques from Peter McIlroy's "Optimistic

      * Sorting and Information Theoretic Complexity", in Proceedings of the

      * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,

      * January 1993.

      *

      * @param a the array to be sorted

      * @param fromIndex the index of the first element (inclusive) to be

      *        sorted

      * @param toIndex the index of the last element (exclusive) to be sorted

      * @param c the comparator to determine the order of the array.  A

      *        {@code null} value indicates that the elements'

      *        {@linkplain Comparable natural ordering} should be used.

      * @throws ClassCastException if the array contains elements that are not

      *         <i>mutually comparable</i> using the specified comparator.

      * @throws IllegalArgumentException if {@code fromIndex > toIndex} or

      *         (optional) if the comparator is found to violate the

      *         {@link Comparator} contract

      * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or

      *         {@code toIndex > a.length}

      */

     public static <T> void sort(T[] a, int fromIndex, int toIndex,

                                 Comparator<? super T> c) {

         if (LegacyMergeSort.userRequested)

             legacyMergeSort(a, fromIndex, toIndex, c);

         else

             TimSort.sort(a, fromIndex, toIndex, c);

     }

     /** To be removed in a future release. */

     private static <T> void legacyMergeSort(T[] a, int fromIndex, int toIndex,

                                             Comparator<? super T> c) {

         rangeCheck(a.length, fromIndex, toIndex);

         T[] aux = copyOfRange(a, fromIndex, toIndex);

         if (c==null)

             mergeSort(aux, a, fromIndex, toIndex, -fromIndex);

         else

             mergeSort(aux, a, fromIndex, toIndex, -fromIndex, c);

     }

     /**

      * Src is the source array that starts at index 0

      * Dest is the (possibly larger) array destination with a possible offset

      * low is the index in dest to start sorting

      * high is the end index in dest to end sorting

      * off is the offset into src corresponding to low in dest

      * To be removed in a future release.

      */

     private static void mergeSort(Object[] src,

                                   Object[] dest,

                                   int low, int high, int off,

                                   Comparator c) {

         int length = high - low;

         // Insertion sort on smallest arrays

         if (length < INSERTIONSORT_THRESHOLD) {

             for (int i=low; i<high; i++)

                 for (int j=i; j>low && c.compare(dest[j-1], dest[j])>0; j--)

                     swap(dest, j, j-1);

             return;

         }

         // Recursively sort halves of dest into src

         int destLow  = low;

         int destHigh = high;

         low  += off;

         high += off;

         int mid = (low + high) >>> 1;

         mergeSort(dest, src, low, mid, -off, c);

         mergeSort(dest, src, mid, high, -off, c);

         // If list is already sorted, just copy from src to dest.  This is an

         // optimization that results in faster sorts for nearly ordered lists.

         if (c.compare(src[mid-1], src[mid]) <= 0) {

            System.arraycopy(src, low, dest, destLow, length);

            return;

         }

         // Merge sorted halves (now in src) into dest

         for(int i = destLow, p = low, q = mid; i < destHigh; i++) {

             if (q >= high || p < mid && c.compare(src[p], src[q]) <= 0)

                 dest[i] = src[p++];

             else

                 dest[i] = src[q++];

         }

     }

     /**

      * Checks that {@code fromIndex} and {@code toIndex} are in

      * the range and throws an appropriate exception, if they aren't.

      */

     private static void rangeCheck(int length, int fromIndex, int toIndex) {

         if (fromIndex > toIndex) {

             throw new IllegalArgumentException(

                 "fromIndex(" + fromIndex + ") > toIndex(" + toIndex + ")");

         }

         if (fromIndex < 0) {

             throw new ArrayIndexOutOfBoundsException(fromIndex);

         }

         if (toIndex > length) {

             throw new ArrayIndexOutOfBoundsException(toIndex);

         }

     }

     // Searching

     /**

      * Searches the specified array of longs for the specified value using the

      * binary search algorithm.  The array must be sorted (as

      * by the {@link #sort(long[])} method) prior to making this call.  If it

      * is not sorted, the results are undefined.  If the array contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      */

     public static int binarySearch(long[] a, long key) {

         return binarySearch0(a, 0, a.length, key);

     }

     /**

      * Searches a range of

      * the specified array of longs for the specified value using the

      * binary search algorithm.

      * The range must be sorted (as

      * by the {@link #sort(long[], int, int)} method)

      * prior to making this call.  If it

      * is not sorted, the results are undefined.  If the range contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static int binarySearch(long[] a, int fromIndex, int toIndex,

                                    long key) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key);

     }

     // Like public version, but without range checks.

     private static int binarySearch0(long[] a, int fromIndex, int toIndex,

                                      long key) {

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             long midVal = a[mid];

             if (midVal < key)

                 low = mid + 1;

             else if (midVal > key)

                 high = mid - 1;

             else

                 return mid; // key found

         }

         return -(low + 1);  // key not found.

     }

     /**

      * Searches the specified array of ints for the specified value using the

      * binary search algorithm.  The array must be sorted (as

      * by the {@link #sort(int[])} method) prior to making this call.  If it

      * is not sorted, the results are undefined.  If the array contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      */

     public static int binarySearch(int[] a, int key) {

         return binarySearch0(a, 0, a.length, key);

     }

     /**

      * Searches a range of

      * the specified array of ints for the specified value using the

      * binary search algorithm.

      * The range must be sorted (as

      * by the {@link #sort(int[], int, int)} method)

      * prior to making this call.  If it

      * is not sorted, the results are undefined.  If the range contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static int binarySearch(int[] a, int fromIndex, int toIndex,

                                    int key) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key);

     }

     // Like public version, but without range checks.

     private static int binarySearch0(int[] a, int fromIndex, int toIndex,

                                      int key) {

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             int midVal = a[mid];

             if (midVal < key)

                 low = mid + 1;

             else if (midVal > key)

                 high = mid - 1;

             else

                 return mid; // key found

         }

         return -(low + 1);  // key not found.

     }

     /**

      * Searches the specified array of shorts for the specified value using

      * the binary search algorithm.  The array must be sorted

      * (as by the {@link #sort(short[])} method) prior to making this call.  If

      * it is not sorted, the results are undefined.  If the array contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      */

     public static int binarySearch(short[] a, short key) {

         return binarySearch0(a, 0, a.length, key);

     }

     /**

      * Searches a range of

      * the specified array of shorts for the specified value using

      * the binary search algorithm.

      * The range must be sorted

      * (as by the {@link #sort(short[], int, int)} method)

      * prior to making this call.  If

      * it is not sorted, the results are undefined.  If the range contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static int binarySearch(short[] a, int fromIndex, int toIndex,

                                    short key) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key);

     }

     // Like public version, but without range checks.

     private static int binarySearch0(short[] a, int fromIndex, int toIndex,

                                      short key) {

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             short midVal = a[mid];

             if (midVal < key)

                 low = mid + 1;

             else if (midVal > key)

                 high = mid - 1;

             else

                 return mid; // key found

         }

         return -(low + 1);  // key not found.

     }

     /**

      * Searches the specified array of chars for the specified value using the

      * binary search algorithm.  The array must be sorted (as

      * by the {@link #sort(char[])} method) prior to making this call.  If it

      * is not sorted, the results are undefined.  If the array contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      */

     public static int binarySearch(char[] a, char key) {

         return binarySearch0(a, 0, a.length, key);

     }

     /**

      * Searches a range of

      * the specified array of chars for the specified value using the

      * binary search algorithm.

      * The range must be sorted (as

      * by the {@link #sort(char[], int, int)} method)

      * prior to making this call.  If it

      * is not sorted, the results are undefined.  If the range contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static int binarySearch(char[] a, int fromIndex, int toIndex,

                                    char key) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key);

     }

     // Like public version, but without range checks.

     private static int binarySearch0(char[] a, int fromIndex, int toIndex,

                                      char key) {

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             char midVal = a[mid];

             if (midVal < key)

                 low = mid + 1;

             else if (midVal > key)

                 high = mid - 1;

             else

                 return mid; // key found

         }

         return -(low + 1);  // key not found.

     }

     /**

      * Searches the specified array of bytes for the specified value using the

      * binary search algorithm.  The array must be sorted (as

      * by the {@link #sort(byte[])} method) prior to making this call.  If it

      * is not sorted, the results are undefined.  If the array contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      */

     public static int binarySearch(byte[] a, byte key) {

         return binarySearch0(a, 0, a.length, key);

     }

     /**

      * Searches a range of

      * the specified array of bytes for the specified value using the

      * binary search algorithm.

      * The range must be sorted (as

      * by the {@link #sort(byte[], int, int)} method)

      * prior to making this call.  If it

      * is not sorted, the results are undefined.  If the range contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static int binarySearch(byte[] a, int fromIndex, int toIndex,

                                    byte key) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key);

     }

     // Like public version, but without range checks.

     private static int binarySearch0(byte[] a, int fromIndex, int toIndex,

                                      byte key) {

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             byte midVal = a[mid];

             if (midVal < key)

                 low = mid + 1;

             else if (midVal > key)

                 high = mid - 1;

             else

                 return mid; // key found

         }

         return -(low + 1);  // key not found.

     }

     /**

      * Searches the specified array of doubles for the specified value using

      * the binary search algorithm.  The array must be sorted

      * (as by the {@link #sort(double[])} method) prior to making this call.

      * If it is not sorted, the results are undefined.  If the array contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.  This method considers all NaN values to be

      * equivalent and equal.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      */

     public static int binarySearch(double[] a, double key) {

         return binarySearch0(a, 0, a.length, key);

     }

     /**

      * Searches a range of

      * the specified array of doubles for the specified value using

      * the binary search algorithm.

      * The range must be sorted

      * (as by the {@link #sort(double[], int, int)} method)

      * prior to making this call.

      * If it is not sorted, the results are undefined.  If the range contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found.  This method considers all NaN values to be

      * equivalent and equal.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static int binarySearch(double[] a, int fromIndex, int toIndex,

                                    double key) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key);

     }

     // Like public version, but without range checks.

     private static int binarySearch0(double[] a, int fromIndex, int toIndex,

                                      double key) {

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             double midVal = a[mid];

             if (midVal < key)

                 low = mid + 1;  // Neither val is NaN, thisVal is smaller

             else if (midVal > key)

                 high = mid - 1; // Neither val is NaN, thisVal is larger

             else {

                 long midBits = Double.doubleToLongBits(midVal);

                 long keyBits = Double.doubleToLongBits(key);

                 if (midBits == keyBits)     // Values are equal

                     return mid;             // Key found

                 else if (midBits < keyBits) // (-0.0, 0.0) or (!NaN, NaN)

                     low = mid + 1;

                 else                        // (0.0, -0.0) or (NaN, !NaN)

                     high = mid - 1;

             }

         }

         return -(low + 1);  // key not found.

     }

     /**

      * Searches the specified array of floats for the specified value using

      * the binary search algorithm. The array must be sorted

      * (as by the {@link #sort(float[])} method) prior to making this call. If

      * it is not sorted, the results are undefined. If the array contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found. This method considers all NaN values to be

      * equivalent and equal.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>. The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key. Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      */

     public static int binarySearch(float[] a, float key) {

         return binarySearch0(a, 0, a.length, key);

     }

     /**

      * Searches a range of

      * the specified array of floats for the specified value using

      * the binary search algorithm.

      * The range must be sorted

      * (as by the {@link #sort(float[], int, int)} method)

      * prior to making this call. If

      * it is not sorted, the results are undefined. If the range contains

      * multiple elements with the specified value, there is no guarantee which

      * one will be found. This method considers all NaN values to be

      * equivalent and equal.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>. The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key. Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static int binarySearch(float[] a, int fromIndex, int toIndex,

                                    float key) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key);

     }

     // Like public version, but without range checks.

     private static int binarySearch0(float[] a, int fromIndex, int toIndex,

                                      float key) {

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             float midVal = a[mid];

             if (midVal < key)

                 low = mid + 1;  // Neither val is NaN, thisVal is smaller

             else if (midVal > key)

                 high = mid - 1; // Neither val is NaN, thisVal is larger

             else {

                 int midBits = Float.floatToIntBits(midVal);

                 int keyBits = Float.floatToIntBits(key);

                 if (midBits == keyBits)     // Values are equal

                     return mid;             // Key found

                 else if (midBits < keyBits) // (-0.0, 0.0) or (!NaN, NaN)

                     low = mid + 1;

                 else                        // (0.0, -0.0) or (NaN, !NaN)

                     high = mid - 1;

             }

         }

         return -(low + 1);  // key not found.

     }

     /**

      * Searches the specified array for the specified object using the binary

      * search algorithm. The array must be sorted into ascending order

      * according to the

      * {@linkplain Comparable natural ordering}

      * of its elements (as by the

      * {@link #sort(Object[])} method) prior to making this call.

      * If it is not sorted, the results are undefined.

      * (If the array contains elements that are not mutually comparable (for

      * example, strings and integers), it <i>cannot</i> be sorted according

      * to the natural ordering of its elements, hence results are undefined.)

      * If the array contains multiple

      * elements equal to the specified object, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws ClassCastException if the search key is not comparable to the

      *         elements of the array.

      */

     public static int binarySearch(Object[] a, Object key) {

         return binarySearch0(a, 0, a.length, key);

     }

     /**

      * Searches a range of

      * the specified array for the specified object using the binary

      * search algorithm.

      * The range must be sorted into ascending order

      * according to the

      * {@linkplain Comparable natural ordering}

      * of its elements (as by the

      * {@link #sort(Object[], int, int)} method) prior to making this

      * call.  If it is not sorted, the results are undefined.

      * (If the range contains elements that are not mutually comparable (for

      * example, strings and integers), it <i>cannot</i> be sorted according

      * to the natural ordering of its elements, hence results are undefined.)

      * If the range contains multiple

      * elements equal to the specified object, there is no guarantee which

      * one will be found.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws ClassCastException if the search key is not comparable to the

      *         elements of the array within the specified range.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static int binarySearch(Object[] a, int fromIndex, int toIndex,

                                    Object key) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key);

     }

     // Like public version, but without range checks.

     private static int binarySearch0(Object[] a, int fromIndex, int toIndex,

                                      Object key) {

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             Comparable midVal = (Comparable)a[mid];

             int cmp = midVal.compareTo(key);

             if (cmp < 0)

                 low = mid + 1;

             else if (cmp > 0)

                 high = mid - 1;

             else

                 return mid; // key found

         }

         return -(low + 1);  // key not found.

     }

     /**

      * Searches the specified array for the specified object using the binary

      * search algorithm.  The array must be sorted into ascending order

      * according to the specified comparator (as by the

      * {@link #sort(Object[], Comparator) sort(T[], Comparator)}

      * method) prior to making this call.  If it is

      * not sorted, the results are undefined.

      * If the array contains multiple

      * elements equal to the specified object, there is no guarantee which one

      * will be found.

      *

      * @param a the array to be searched

      * @param key the value to be searched for

      * @param c the comparator by which the array is ordered.  A

      *        <tt>null</tt> value indicates that the elements'

      *        {@linkplain Comparable natural ordering} should be used.

      * @return index of the search key, if it is contained in the array;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element greater than the key, or <tt>a.length</tt> if all

      *         elements in the array are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws ClassCastException if the array contains elements that are not

      *         <i>mutually comparable</i> using the specified comparator,

      *         or the search key is not comparable to the

      *         elements of the array using this comparator.

      */

     public static <T> int binarySearch(T[] a, T key, Comparator<? super T> c) {

         return binarySearch0(a, 0, a.length, key, c);

     }

     /**

      * Searches a range of

      * the specified array for the specified object using the binary

      * search algorithm.

      * The range must be sorted into ascending order

      * according to the specified comparator (as by the

      * {@link #sort(Object[], int, int, Comparator)

      * sort(T[], int, int, Comparator)}

      * method) prior to making this call.

      * If it is not sorted, the results are undefined.

      * If the range contains multiple elements equal to the specified object,

      * there is no guarantee which one will be found.

      *

      * @param a the array to be searched

      * @param fromIndex the index of the first element (inclusive) to be

      *          searched

      * @param toIndex the index of the last element (exclusive) to be searched

      * @param key the value to be searched for

      * @param c the comparator by which the array is ordered.  A

      *        <tt>null</tt> value indicates that the elements'

      *        {@linkplain Comparable natural ordering} should be used.

      * @return index of the search key, if it is contained in the array

      *         within the specified range;

      *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The

      *         <i>insertion point</i> is defined as the point at which the

      *         key would be inserted into the array: the index of the first

      *         element in the range greater than the key,

      *         or <tt>toIndex</tt> if all

      *         elements in the range are less than the specified key.  Note

      *         that this guarantees that the return value will be >= 0 if

      *         and only if the key is found.

      * @throws ClassCastException if the range contains elements that are not

      *         <i>mutually comparable</i> using the specified comparator,

      *         or the search key is not comparable to the

      *         elements in the range using this comparator.

      * @throws IllegalArgumentException

      *         if {@code fromIndex > toIndex}

      * @throws ArrayIndexOutOfBoundsException

      *         if {@code fromIndex < 0 or toIndex > a.length}

      * @since 1.6

      */

     public static <T> int binarySearch(T[] a, int fromIndex, int toIndex,

                                        T key, Comparator<? super T> c) {

         rangeCheck(a.length, fromIndex, toIndex);

         return binarySearch0(a, fromIndex, toIndex, key, c);

     }

     // Like public version, but without range checks.

     private static <T> int binarySearch0(T[] a, int fromIndex, int toIndex,

                                          T key, Comparator<? super T> c) {

         if (c == null) {

             return binarySearch0(a, fromIndex, toIndex, key);

         }

         int low = fromIndex;

         int high = toIndex - 1;

         while (low <= high) {

             int mid = (low + high) >>> 1;

             T midVal = a[mid];

             int cmp = c.compare(midVal, key);

             if (cmp < 0)

                 low = mid + 1;

             else if (cmp > 0)

                 high = mid - 1;

             else

                 return mid; // key found

         }

         return -(low + 1);  // key not found.

     }

     // Equality Testing

     /**

      * Returns <tt>true</tt> if the two specified arrays of longs are

      * <i>equal</i> to one another.  Two arrays are considered equal if both

      * arrays contain the same number of elements, and all corresponding pairs

      * of elements in the two arrays are equal.  In other words, two arrays

      * are equal if they contain the same elements in the same order.  Also,

      * two array references are considered equal if both are <tt>null</tt>.<p>

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      */

     public static boolean equals(long[] a, long[] a2) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++)

             if (a[i] != a2[i])

                 return false;

         return true;

     }

     /**

      * Returns <tt>true</tt> if the two specified arrays of ints are

      * <i>equal</i> to one another.  Two arrays are considered equal if both

      * arrays contain the same number of elements, and all corresponding pairs

      * of elements in the two arrays are equal.  In other words, two arrays

      * are equal if they contain the same elements in the same order.  Also,

      * two array references are considered equal if both are <tt>null</tt>.<p>

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      */

     public static boolean equals(int[] a, int[] a2) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++)

             if (a[i] != a2[i])

                 return false;

         return true;

     }

     /**

      * Returns <tt>true</tt> if the two specified arrays of shorts are

      * <i>equal</i> to one another.  Two arrays are considered equal if both

      * arrays contain the same number of elements, and all corresponding pairs

      * of elements in the two arrays are equal.  In other words, two arrays

      * are equal if they contain the same elements in the same order.  Also,

      * two array references are considered equal if both are <tt>null</tt>.<p>

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      */

     public static boolean equals(short[] a, short a2[]) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++)

             if (a[i] != a2[i])

                 return false;

         return true;

     }

     /**

      * Returns <tt>true</tt> if the two specified arrays of chars are

      * <i>equal</i> to one another.  Two arrays are considered equal if both

      * arrays contain the same number of elements, and all corresponding pairs

      * of elements in the two arrays are equal.  In other words, two arrays

      * are equal if they contain the same elements in the same order.  Also,

      * two array references are considered equal if both are <tt>null</tt>.<p>

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      */

     public static boolean equals(char[] a, char[] a2) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++)

             if (a[i] != a2[i])

                 return false;

         return true;

     }

     /**

      * Returns <tt>true</tt> if the two specified arrays of bytes are

      * <i>equal</i> to one another.  Two arrays are considered equal if both

      * arrays contain the same number of elements, and all corresponding pairs

      * of elements in the two arrays are equal.  In other words, two arrays

      * are equal if they contain the same elements in the same order.  Also,

      * two array references are considered equal if both are <tt>null</tt>.<p>

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      */

     public static boolean equals(byte[] a, byte[] a2) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++)

             if (a[i] != a2[i])

                 return false;

         return true;

     }

     /**

      * Returns <tt>true</tt> if the two specified arrays of booleans are

      * <i>equal</i> to one another.  Two arrays are considered equal if both

      * arrays contain the same number of elements, and all corresponding pairs

      * of elements in the two arrays are equal.  In other words, two arrays

      * are equal if they contain the same elements in the same order.  Also,

      * two array references are considered equal if both are <tt>null</tt>.<p>

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      */

     public static boolean equals(boolean[] a, boolean[] a2) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++)

             if (a[i] != a2[i])

                 return false;

         return true;

     }

     /**

      * Returns <tt>true</tt> if the two specified arrays of doubles are

      * <i>equal</i> to one another.  Two arrays are considered equal if both

      * arrays contain the same number of elements, and all corresponding pairs

      * of elements in the two arrays are equal.  In other words, two arrays

      * are equal if they contain the same elements in the same order.  Also,

      * two array references are considered equal if both are <tt>null</tt>.<p>

      *

      * Two doubles <tt>d1</tt> and <tt>d2</tt> are considered equal if:

      * <pre>    <tt>new Double(d1).equals(new Double(d2))</tt></pre>

      * (Unlike the <tt>==</tt> operator, this method considers

      * <tt>NaN</tt> equals to itself, and 0.0d unequal to -0.0d.)

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      * @see Double#equals(Object)

      */

     public static boolean equals(double[] a, double[] a2) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++)

             if (Double.doubleToLongBits(a[i])!=Double.doubleToLongBits(a2[i]))

                 return false;

         return true;

     }

     /**

      * Returns <tt>true</tt> if the two specified arrays of floats are

      * <i>equal</i> to one another.  Two arrays are considered equal if both

      * arrays contain the same number of elements, and all corresponding pairs

      * of elements in the two arrays are equal.  In other words, two arrays

      * are equal if they contain the same elements in the same order.  Also,

      * two array references are considered equal if both are <tt>null</tt>.<p>

      *

      * Two floats <tt>f1</tt> and <tt>f2</tt> are considered equal if:

      * <pre>    <tt>new Float(f1).equals(new Float(f2))</tt></pre>

      * (Unlike the <tt>==</tt> operator, this method considers

      * <tt>NaN</tt> equals to itself, and 0.0f unequal to -0.0f.)

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      * @see Float#equals(Object)

      */

     public static boolean equals(float[] a, float[] a2) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++)

             if (Float.floatToIntBits(a[i])!=Float.floatToIntBits(a2[i]))

                 return false;

         return true;

     }

     /**

      * Returns <tt>true</tt> if the two specified arrays of Objects are

      * <i>equal</i> to one another.  The two arrays are considered equal if

      * both arrays contain the same number of elements, and all corresponding

      * pairs of elements in the two arrays are equal.  Two objects <tt>e1</tt>

      * and <tt>e2</tt> are considered <i>equal</i> if <tt>(e1==null ? e2==null

      * : e1.equals(e2))</tt>.  In other words, the two arrays are equal if

      * they contain the same elements in the same order.  Also, two array

      * references are considered equal if both are <tt>null</tt>.<p>

      *

      * @param a one array to be tested for equality

      * @param a2 the other array to be tested for equality

      * @return <tt>true</tt> if the two arrays are equal

      */

     public static boolean equals(Object[] a, Object[] a2) {

         if (a==a2)

             return true;

         if (a==null || a2==null)

             return false;

         int length = a.length;

         if (a2.length != length)

             return false;

         for (int i=0; i<length; i++) {

             Object o1 = a[i];

             Object o2 = a2[i];

             if (!(o1==null ? o2==null : o1.equals(o2)))

                 return false;

         }

         return true;

     }

     // Filling

     /**

      * Assigns the specified long value to each element of the specified array

      * of longs.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      */

     public static void fill(long[] a, long val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified long value to each element of the specified

      * range of the specified array of longs.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      */

     public static void fill(long[] a, int fromIndex, int toIndex, long val) {

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified int value to each element of the specified array

      * of ints.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      */

     public static void fill(int[] a, int val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified int value to each element of the specified

      * range of the specified array of ints.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      */

     public static void fill(int[] a, int fromIndex, int toIndex, int val) {

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified short value to each element of the specified array

      * of shorts.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      */

     public static void fill(short[] a, short val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified short value to each element of the specified

      * range of the specified array of shorts.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      */

     public static void fill(short[] a, int fromIndex, int toIndex, short val) {

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified char value to each element of the specified array

      * of chars.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      */

     public static void fill(char[] a, char val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified char value to each element of the specified

      * range of the specified array of chars.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      */

     public static void fill(char[] a, int fromIndex, int toIndex, char val) {

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified byte value to each element of the specified array

      * of bytes.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      */

     public static void fill(byte[] a, byte val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified byte value to each element of the specified

      * range of the specified array of bytes.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      */

     public static void fill(byte[] a, int fromIndex, int toIndex, byte val) {

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified boolean value to each element of the specified

      * array of booleans.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      */

     public static void fill(boolean[] a, boolean val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified boolean value to each element of the specified

      * range of the specified array of booleans.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      */

     public static void fill(boolean[] a, int fromIndex, int toIndex,

                             boolean val) {

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified double value to each element of the specified

      * array of doubles.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      */

     public static void fill(double[] a, double val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified double value to each element of the specified

      * range of the specified array of doubles.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      */

     public static void fill(double[] a, int fromIndex, int toIndex,double val){

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified float value to each element of the specified array

      * of floats.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      */

     public static void fill(float[] a, float val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified float value to each element of the specified

      * range of the specified array of floats.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      */

     public static void fill(float[] a, int fromIndex, int toIndex, float val) {

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified Object reference to each element of the specified

      * array of Objects.

      *

      * @param a the array to be filled

      * @param val the value to be stored in all elements of the array

      * @throws ArrayStoreException if the specified value is not of a

      *         runtime type that can be stored in the specified array

      */

     public static void fill(Object[] a, Object val) {

         for (int i = 0, len = a.length; i < len; i++)

             a[i] = val;

     }

     /**

      * Assigns the specified Object reference to each element of the specified

      * range of the specified array of Objects.  The range to be filled

      * extends from index <tt>fromIndex</tt>, inclusive, to index

      * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the

      * range to be filled is empty.)

      *

      * @param a the array to be filled

      * @param fromIndex the index of the first element (inclusive) to be

      *        filled with the specified value

      * @param toIndex the index of the last element (exclusive) to be

      *        filled with the specified value

      * @param val the value to be stored in all elements of the array

      * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>

      * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or

      *         <tt>toIndex &gt; a.length</tt>

      * @throws ArrayStoreException if the specified value is not of a

      *         runtime type that can be stored in the specified array

      */

     public static void fill(Object[] a, int fromIndex, int toIndex, Object val) {

         rangeCheck(a.length, fromIndex, toIndex);

         for (int i = fromIndex; i < toIndex; i++)

             a[i] = val;

     }

     // Cloning

     /**

      * Copies the specified array, truncating or padding with nulls (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>null</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      * The resulting array is of exactly the same class as the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with nulls

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static <T> T[] copyOf(T[] original, int newLength) {

         return (T[]) copyOf(original, newLength, original.getClass());

     }

     /**

      * Copies the specified array, truncating or padding with nulls (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>null</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      * The resulting array is of the class <tt>newType</tt>.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @param newType the class of the copy to be returned

      * @return a copy of the original array, truncated or padded with nulls

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @throws ArrayStoreException if an element copied from

      *     <tt>original</tt> is not of a runtime type that can be stored in

      *     an array of class <tt>newType</tt>

      * @since 1.6

      */

     public static <T,U> T[] copyOf(U[] original, int newLength, Class<? extends T[]> newType) {

         T[] copy = ((Object)newType == (Object)Object[].class)

             ? (T[]) new Object[newLength]

             : (T[]) Array.newInstance(newType.getComponentType(), newLength);

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified array, truncating or padding with zeros (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>(byte)0</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with zeros

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static byte[] copyOf(byte[] original, int newLength) {

         byte[] copy = new byte[newLength];

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified array, truncating or padding with zeros (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>(short)0</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with zeros

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static short[] copyOf(short[] original, int newLength) {

         short[] copy = new short[newLength];

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified array, truncating or padding with zeros (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>0</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with zeros

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static int[] copyOf(int[] original, int newLength) {

         int[] copy = new int[newLength];

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified array, truncating or padding with zeros (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>0L</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with zeros

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static long[] copyOf(long[] original, int newLength) {

         long[] copy = new long[newLength];

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified array, truncating or padding with null characters (if necessary)

      * so the copy has the specified length.  For all indices that are valid

      * in both the original array and the copy, the two arrays will contain

      * identical values.  For any indices that are valid in the copy but not

      * the original, the copy will contain <tt>'\\u000'</tt>.  Such indices

      * will exist if and only if the specified length is greater than that of

      * the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with null characters

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static char[] copyOf(char[] original, int newLength) {

         char[] copy = new char[newLength];

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified array, truncating or padding with zeros (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>0f</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with zeros

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static float[] copyOf(float[] original, int newLength) {

         float[] copy = new float[newLength];

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified array, truncating or padding with zeros (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>0d</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with zeros

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static double[] copyOf(double[] original, int newLength) {

         double[] copy = new double[newLength];

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified array, truncating or padding with <tt>false</tt> (if necessary)

      * so the copy has the specified length.  For all indices that are

      * valid in both the original array and the copy, the two arrays will

      * contain identical values.  For any indices that are valid in the

      * copy but not the original, the copy will contain <tt>false</tt>.

      * Such indices will exist if and only if the specified length

      * is greater than that of the original array.

      *

      * @param original the array to be copied

      * @param newLength the length of the copy to be returned

      * @return a copy of the original array, truncated or padded with false elements

      *     to obtain the specified length

      * @throws NegativeArraySizeException if <tt>newLength</tt> is negative

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static boolean[] copyOf(boolean[] original, int newLength) {

         boolean[] copy = new boolean[newLength];

         System.arraycopy(original, 0, copy, 0,

                          Math.min(original.length, newLength));

         return copy;

     }

     /**

      * Copies the specified range of the specified array into a new array.

      * The initial index of the range (<tt>from</tt>) must lie between zero

      * and <tt>original.length</tt>, inclusive.  The value at

      * <tt>original[from]</tt> is placed into the initial element of the copy

      * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).

      * Values from subsequent elements in the original array are placed into

      * subsequent elements in the copy.  The final index of the range

      * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,

      * may be greater than <tt>original.length</tt>, in which case

      * <tt>null</tt> is placed in all elements of the copy whose index is

      * greater than or equal to <tt>original.length - from</tt>.  The length

      * of the returned array will be <tt>to - from</tt>.

      * <p>

      * The resulting array is of exactly the same class as the original array.

      *

      * @param original the array from which a range is to be copied

      * @param from the initial index of the range to be copied, inclusive

      * @param to the final index of the range to be copied, exclusive.

      *     (This index may lie outside the array.)

      * @return a new array containing the specified range from the original array,

      *     truncated or padded with nulls to obtain the required length

      * @throws ArrayIndexOutOfBoundsException if {@code from < 0}

      *     or {@code from > original.length}

      * @throws IllegalArgumentException if <tt>from &gt; to</tt>

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static <T> T[] copyOfRange(T[] original, int from, int to) {

         return copyOfRange(original, from, to, (Class<T[]>) original.getClass());

     }

     /**

      * Copies the specified range of the specified array into a new array.

      * The initial index of the range (<tt>from</tt>) must lie between zero

      * and <tt>original.length</tt>, inclusive.  The value at

      * <tt>original[from]</tt> is placed into the initial element of the copy

      * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).

      * Values from subsequent elements in the original array are placed into

      * subsequent elements in the copy.  The final index of the range

      * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,

      * may be greater than <tt>original.length</tt>, in which case

      * <tt>null</tt> is placed in all elements of the copy whose index is

      * greater than or equal to <tt>original.length - from</tt>.  The length

      * of the returned array will be <tt>to - from</tt>.

      * The resulting array is of the class <tt>newType</tt>.

      *

      * @param original the array from which a range is to be copied

      * @param from the initial index of the range to be copied, inclusive

      * @param to the final index of the range to be copied, exclusive.

      *     (This index may lie outside the array.)

      * @param newType the class of the copy to be returned

      * @return a new array containing the specified range from the original array,

      *     truncated or padded with nulls to obtain the required length

      * @throws ArrayIndexOutOfBoundsException if {@code from < 0}

      *     or {@code from > original.length}

      * @throws IllegalArgumentException if <tt>from &gt; to</tt>

      * @throws NullPointerException if <tt>original</tt> is null

      * @throws ArrayStoreException if an element copied from

      *     <tt>original</tt> is not of a runtime type that can be stored in

      *     an array of class <tt>newType</tt>.

      * @since 1.6

      */

     public static <T,U> T[] copyOfRange(U[] original, int from, int to, Class<? extends T[]> newType) {

         int newLength = to - from;

         if (newLength < 0)

             throw new IllegalArgumentException(from + " > " + to);

         T[] copy = ((Object)newType == (Object)Object[].class)

             ? (T[]) new Object[newLength]

             : (T[]) Array.newInstance(newType.getComponentType(), newLength);

         System.arraycopy(original, from, copy, 0,

                          Math.min(original.length - from, newLength));

         return copy;

     }

     /**

      * Copies the specified range of the specified array into a new array.

      * The initial index of the range (<tt>from</tt>) must lie between zero

      * and <tt>original.length</tt>, inclusive.  The value at

      * <tt>original[from]</tt> is placed into the initial element of the copy

      * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).

      * Values from subsequent elements in the original array are placed into

      * subsequent elements in the copy.  The final index of the range

      * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,

      * may be greater than <tt>original.length</tt>, in which case

      * <tt>(byte)0</tt> is placed in all elements of the copy whose index is

      * greater than or equal to <tt>original.length - from</tt>.  The length

      * of the returned array will be <tt>to - from</tt>.

      *

      * @param original the array from which a range is to be copied

      * @param from the initial index of the range to be copied, inclusive

      * @param to the final index of the range to be copied, exclusive.

      *     (This index may lie outside the array.)

      * @return a new array containing the specified range from the original array,

      *     truncated or padded with zeros to obtain the required length

      * @throws ArrayIndexOutOfBoundsException if {@code from < 0}

      *     or {@code from > original.length}

      * @throws IllegalArgumentException if <tt>from &gt; to</tt>

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static byte[] copyOfRange(byte[] original, int from, int to) {

         int newLength = to - from;

         if (newLength < 0)

             throw new IllegalArgumentException(from + " > " + to);

         byte[] copy = new byte[newLength];

         System.arraycopy(original, from, copy, 0,

                          Math.min(original.length - from, newLength));

         return copy;

     }

     /**

      * Copies the specified range of the specified array into a new array.

      * The initial index of the range (<tt>from</tt>) must lie between zero

      * and <tt>original.length</tt>, inclusive.  The value at

      * <tt>original[from]</tt> is placed into the initial element of the copy

      * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).

      * Values from subsequent elements in the original array are placed into

      * subsequent elements in the copy.  The final index of the range

      * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,

      * may be greater than <tt>original.length</tt>, in which case

      * <tt>(short)0</tt> is placed in all elements of the copy whose index is

      * greater than or equal to <tt>original.length - from</tt>.  The length

      * of the returned array will be <tt>to - from</tt>.

      *

      * @param original the array from which a range is to be copied

      * @param from the initial index of the range to be copied, inclusive

      * @param to the final index of the range to be copied, exclusive.

      *     (This index may lie outside the array.)

      * @return a new array containing the specified range from the original array,

      *     truncated or padded with zeros to obtain the required length

      * @throws ArrayIndexOutOfBoundsException if {@code from < 0}

      *     or {@code from > original.length}

      * @throws IllegalArgumentException if <tt>from &gt; to</tt>

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static short[] copyOfRange(short[] original, int from, int to) {

         int newLength = to - from;

         if (newLength < 0)

             throw new IllegalArgumentException(from + " > " + to);

         short[] copy = new short[newLength];

         System.arraycopy(original, from, copy, 0,

                          Math.min(original.length - from, newLength));

         return copy;

     }

     /**

      * Copies the specified range of the specified array into a new array.

      * The initial index of the range (<tt>from</tt>) must lie between zero

      * and <tt>original.length</tt>, inclusive.  The value at

      * <tt>original[from]</tt> is placed into the initial element of the copy

      * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).

      * Values from subsequent elements in the original array are placed into

      * subsequent elements in the copy.  The final index of the range

      * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,

      * may be greater than <tt>original.length</tt>, in which case

      * <tt>0</tt> is placed in all elements of the copy whose index is

      * greater than or equal to <tt>original.length - from</tt>.  The length

      * of the returned array will be <tt>to - from</tt>.

      *

      * @param original the array from which a range is to be copied

      * @param from the initial index of the range to be copied, inclusive

      * @param to the final index of the range to be copied, exclusive.

      *     (This index may lie outside the array.)

      * @return a new array containing the specified range from the original array,

      *     truncated or padded with zeros to obtain the required length

      * @throws ArrayIndexOutOfBoundsException if {@code from < 0}

      *     or {@code from > original.length}

      * @throws IllegalArgumentException if <tt>from &gt; to</tt>

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static int[] copyOfRange(int[] original, int from, int to) {

         int newLength = to - from;

         if (newLength < 0)

             throw new IllegalArgumentException(from + " > " + to);

         int[] copy = new int[newLength];

         System.arraycopy(original, from, copy, 0,

                          Math.min(original.length - from, newLength));

         return copy;

     }

     /**

      * Copies the specified range of the specified array into a new array.

      * The initial index of the range (<tt>from</tt>) must lie between zero

      * and <tt>original.length</tt>, inclusive.  The value at

      * <tt>original[from]</tt> is placed into the initial element of the copy

      * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).

      * Values from subsequent elements in the original array are placed into

      * subsequent elements in the copy.  The final index of the range

      * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,

      * may be greater than <tt>original.length</tt>, in which case

      * <tt>0L</tt> is placed in all elements of the copy whose index is

      * greater than or equal to <tt>original.length - from</tt>.  The length

      * of the returned array will be <tt>to - from</tt>.

      *

      * @param original the array from which a range is to be copied

      * @param from the initial index of the range to be copied, inclusive

      * @param to the final index of the range to be copied, exclusive.

      *     (This index may lie outside the array.)

      * @return a new array containing the specified range from the original array,

      *     truncated or padded with zeros to obtain the required length

      * @throws ArrayIndexOutOfBoundsException if {@code from < 0}

      *     or {@code from > original.length}

      * @throws IllegalArgumentException if <tt>from &gt; to</tt>

      * @throws NullPointerException if <tt>original</tt> is null

      * @since 1.6

      */

     public static long[] copyOfRange(long[] original, int from, int to) {

         int newLength = to - from;